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Intervals in the Hales-Jewett theorem

Abstract:
The Hales–Jewett theorem states that for any m and r there exists an n such that any r-colouring of the elements of [m]n contains a monochromatic combinatorial line. We study the structure of the wildcard set S ⊆ [n] which determines this monochromatic line, showing that when r is odd there are r-colourings of [3]n where the wildcard set of a monochromatic line cannot be the union of fewer than r intervals. This is tight, as for n sufficiently large there are always monochromatic lines whose wildcard set is the union of at most r intervals.
Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Wadham College
ORCID:
0000-0001-5899-1829
Kamčev, N More by this author
Publisher:
Elsevier Publisher's website
Journal:
European Journal of Combinatorics Journal website
Acceptance date:
2018-10-08
EISSN:
1095-9971
ISSN:
0195-6698
Pubs id:
pubs:924626
URN:
uri:fafec88b-a9e8-4d5b-b72b-2fb70d819ebc
UUID:
uuid:fafec88b-a9e8-4d5b-b72b-2fb70d819ebc
Local pid:
pubs:924626

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